A Gaia DR2 Mock Stellar Catalog

Galaxia is a tool that allows one to sample stars from the Besançon Galactic model (Robin et al. 2003), using a specific set of stellar isochrones to obtain their astrophysical parameters. The Galactic warp was switched on during the simulations and the solar zero-point was set to (X, Y, Z) = (−8.0, 0.0, 0.015) kpc and the velocities to $(U,V,W)=(11.1,239.08,7.25)\mathrm{km}{{\rm{s}}}^{-1}$. Transformations from phase-space to observable coordinates on the sky (ra, dec, pm_ra_cosdec, pm_dec and radial_velocity) were done using astropy⁶ (The Astropy Collaboration et al. 2018). And we used the latest PARSEC isochrones⁷ —PARSEC v1.2S+ COLIBRI PR16 (Bressan et al. 2012; Marigo et al. 2017; Rosenfield et al. 2016; Marigo et al. 2013)—which also provide photometric values for each star using the nominal Gaia DR1 photometric bands G, BP, and RP (Jordi et al. 2010). GDR2 passbands where not available during the construction of this catalog.

At this stage, we were already able to account for the magnitude limit of Gaia and only selected stars with apparent magnitude brighter than G = 20.7 mag, which preliminarily resulted in over six billion sources.

A crucial step in transforming a Galaxia simulation into a catalog resembling actual observations is the application of a dust distribution, which will change the apparent colors and luminosities of the stars.

Because the Gaia photometric bands span a broad wavelength range (∼300 nm), the simple conversion of extinction coefficients from e.g., Schlafly & Finkbeiner (2011, Table 6) to reddening and extinction into the Gaia bands, e.g., A_G, is only a poor approximation and may lead to significant inconsistency across the broad range of stellar spectra. Instead we must account for non-linearities in particular with respect to the stars' colors. Fortunately, the PARSEC isochrones also provide dust-attenuated photometry in various photometric systems, including the Gaia passbands (DR1, nominal passbands).

To include a realistic dust distribution on the Galaxia model, we used the combined 3D extinction map from Bovy et al. (2016), through its python package mwdust⁸ , which is capable of returning line-of-sight extinctions when provided with sky coordinates and distances. This 3D dust map combines the results of Marshall et al. (2006); Green et al. (2015), and Drimmel et al. (2003) and it provides E(B-V)_SFD values on the scale defined in Schlegel et al. (1998).⁹ As discussed in Schlafly & Finkbeiner (2011), the E(B-V)_SFD scale overestimates the extinction by 14% with respect to their own findings. Hence we corrected for this overestimation and adopted the prescription associated with the PARSEC isochrones of Cardelli et al. (1989); O'Donnell (1994) with R₀ = 3.1 to derive the monochromatic extinction (in mag) at wavelength λ = 547.7 nm as

$$\begin{eqnarray}&&{{\rm{A}}}_{0}=3.1\times {\rm{E}}{({\rm{B}}-{\rm{V}})}_{\mathrm{SFD}}\times 0.86.\end{eqnarray} \tag{ 1 }$$

Matching each star from Galaxia to an isochrone and a proper amount of extinction is a challenging task for 6 billion stars. Instead, we approximated each star to its closest match from a precomputed collection of dust-attenuated stellar isochrones. The grid spans A₀ values ranging from 0 to 15 mag with in steps of 0.025 mag (for stars with even higher extinction we linearly extrapolated the extinction values) and [Fe/H] values from −2 to 0.5 dex in steps of 0.25 dex. We further bin in $\mathrm{log}({{\rm{T}}}_{\mathrm{eff}})$ in 0.02 dex steps and $\mathrm{log}(\mathrm{lum})$ in 0.2 dex steps on a star-by-star basis. Each star in our catalog is associated with an index_parsec number that records this matching step and maps each star onto the grid of isochrones and thus allows us to query photometric measurements in other bands from the supplementary parsec photometry and extinction table. Figure 1 shows the resulting color–magnitude and absolute magnitude diagrams of the resulting final data set (applying Gaia selection after accounting for the dust attenuation).

The following ADQL query provides the data to plot the left panel of Figure 1:

As the latest PARSEC models (v1.2S + COLIBRI) did not provide dust-attenuated photometry when this catalog was drawn up, we had to match the previous version, PARSEC1.2S (Chen et al. 2014; Tang et al. 2014; Chen et al. 2015) to Galaxia, based on PARSEC v1.2S+ isochrones. This inconsistency affects only a limited range of evolution phases that were deeply revised between the two sets of isochrones (e.g., O stars, TP-AGB).

Our catalog provides apparent magnitudes in the nominal DR1 passbands¹⁰ G, BP, and RP. In addition, we provide an additional table, which can be used to obtain photometry for UBVRIJHK (Bessell & Brett 1988; Bessell 1990; Maíz Apellániz 2006), SDSS (Fukugita et al. 1996), 2MASS (Cohen et al. 2003), and WISE¹¹ (Wright et al. 2010) to a precision of ≈0.1 mag. This uncertainty mainly arises from the finite resolution of the isochrone grid we used, which corresponds to 0.2 dex spacing in log-luminosity. With actual GDR2 data, those would be obtained with catalog cross-matching, which of course is not possible with a mock catalog and its random realization of the actual star positions.

The following query illustrates how to obtain complementary photometry (e.g., 2MASS) to the main GDR2mock catalog:

All values provided in the mock catalog are noise-free. As a result, there are no negative parallaxes and the parallaxes can be directly inverted to give exact model distances. To obtain noisy mock observations, one should sample any quantity, say the parallax measurement, from a Gaussian with the true parallax as mean and the parallax_error as the standard deviation. To enable this we provide in the catalog astrometric and photometric-uncertainty estimates based on the nominal uncertainty model¹² (de Bruijne 2005) scaled to the duration of the data segment in GDR2 (which is about 668 days or 37% of the 5 year nominal mission duration). This nominal model depends also on the ecliptic latitude, β (which enters via an averaged version of the scanning law). We assume an uncertainty scaling relation of $\tfrac{1}{\sqrt{n}}$ with the number of observations, n, for parallaxes, positions, proper motions and magnitudes, neglecting the noise floors and slightly different scaling for the proper motions based on official communication.

More specifically, we use an approximation of the Gaia scanning law (scaled to the 22 month data segment) that gives us the number of observations, n, as a function of ecliptic latitude in 20 bins.¹³ To calculate the parallax uncertainty we use the nominal end-of-mission (eom) parallax uncertainty, ${\sigma }_{\varpi ,\mathrm{eom}}(G,V-I)$, multiply it by the ecliptic latitude dependent uncertainty factor ${{\rm{x}}}_{\varpi }(| \sin (\beta )| )$ (https://www.cosmos.esa.int/web/gaia/table-6 which includes the nominal number of observations) and rescale with the shortened 37% baseline:

$$\begin{eqnarray}&&{\sigma }_{\varpi }={\sigma }_{\varpi ,\mathrm{eom}}\times \displaystyle \frac{{{\rm{x}}}_{\varpi }}{\sqrt{0.37}}.\end{eqnarray} \tag{ 2 }$$

We do the same with the positions and proper motions, which are also related to ${\sigma }_{\varpi ,\mathrm{eom}}$, but have their own ecliptic latitude dependent uncertainty factors provided by the abovementioned online Table 6.

For the nominal single-transit (st) photometric uncertainty ${\sigma }_{{\rm{G}},\mathrm{st}}(G)$ and ${\sigma }_{\mathrm{BP},\mathrm{RP},\mathrm{st}}(G,V-I)$ we simply scale with 1 over the square root of number of observations,

$$\begin{eqnarray}&&{\sigma }_{{\rm{X}}}=\displaystyle \frac{{\sigma }_{{\rm{X}},\mathrm{st}}}{\sqrt{n}},\end{eqnarray} \tag{ 3 }$$

where X denotes the respective photometric band, i.e., BP, RP, or G.

We do not provide uncertainty estimates for the radial velocity, but the interested reader is referred to Gaia Collaboration et al. (2018).

A complete simulation of the Milky Way, such as Galaxia, offers not only exact phase-space information of the stars and prediction of their photometric properties, but also of their underlying physical parameters: ages, masses, metallicities, gravities, luminosities, and effective temperatures, etc. These underlying stellar parameters should prove useful in tuning cuts in observables (e.g., color, magnitude and parallax) to optimize for a specific target stellar population (e.g., OB stars, stars with high extinction, old metal-rich stars etc.), and we include them in this mock catalog. Note that GDR2 will provide observational quantities for some of these stellar parameters, which were derived for sources with G ≤ 17 mag from the Gaia photometry and parallax measurements (Andrae et al. 2018), namely, effective temperature for some 161 million sources, line-of-sight extinction and the reddening, for 88 million sources, and luminosity and radius for 77 million sources.

Our catalog contains a total number of stars of 1 606 747 035, when matching the approximate flux limits of Gaia. The actual data model of our catalog can be inspected here: http://dc.g-vo.org/tableinfo/gdr2mock.main, mimicking by design the GDR2 data model¹⁴ : fields and associated names as well as their units. Note, however, that not all columns that appear in DR2 are filled in our catalog and that we provide a few additional ones. Specifically,

• Nobs is added, reflecting the nominal ecliptic latitude dependent number of visits for GDR2.
• Age, mass, feh, logg and a0 are added, while luminosity, effective temperature, A_G, E(BP-RP) and radius are filled into their respective Apsis (Bailer-Jones et al. 2013) fields: teff_val, a_g_val, e_bp_min_rp_val, lum_val and radius_val. Beware that in DR2 these are only provided for a subset of stars with G ≤ 17 mag (cf. Andrae et al. 2018), whereas in our mock catalog we provide entries for all sources.
• Index_parsec is an index for joining the main mock catalog to other photometric bands/extinctions in the gdr2mock.photometry table.

Similarly to GDR2, we also provide

• Random_index is an integer ranging from 0 to 1 606 747 034, the total number of stars in the mock catalog minus one. This index is useful to create random subsamples representative of the entire catalog.
• Source_id follows the Gaia referencing scheme. It is primarily the healpix¹⁵ number using NSIDE = 4096 with the nested scheme in equatorial coordinates multiplied by 2³⁵. The remaining digits of source_id are reserved for a running number that serves as a unique identifier per healpix cell. Unlike Gaia no bits are reserved for Data Processing Center identification. Still the source_id can be easily turned into healpix number for any arbitrary healpix level smaller than 12 (level 12 corresponding to Nside = 4096) via division:
  $$\begin{eqnarray}&&\mathrm{Healpix}(\mathrm{level}=n)=\displaystyle \frac{{\mathtt{source}}\_{\mathtt{id}}}{{2}^{35}\times {4}^{(12-n)}}.\end{eqnarray} \tag{ 4 }$$

The table is available through GAVO's TAP service¹⁶ and is registered in the VO registry as ivo://org.gavo.dc/gdr2mock/q/main. The full catalog will be hosted by GAVO for at least six month and potentially until GDR3. In the long term there will be a subsample hosted by GAVO which will be cut using the first 10% stars according to the random_index. However, a bulk download of the complete catalog (without time limitations) is available as FITS binary tables from the reference URL.¹⁷

The GDR2mock main table is instantiated using a view (resembling the GDR2 data model) of the actual FITS files. This is why the indexed columns are not marked as such in the gdr2mock.main table but instead in the gdr2mock.generated_data table. Indexed and therefore fast to query columns are: ra, dec, l, b, pmra, pmdec, phot_g_mean_mag, phot_bp_mean_mag, phot_rp_mean_mag, source_id and random_index.

It is also planned to host the complete catalog on the Gaia archive (https://gea.esac.esa.int/archive/).

This mock catalog has obvious scientific limitations that stem both from the underlying Milky Way model and from our generation of mock observables.

Galaxia is simulating neither stellar binaries nor stellar remnants, which will appear in the Gaia data. The phase-space distributions of the stars are assumed smooth and therefore does not generate phase-space or configuration-space clustering. The model does not account for extragalactic systems, including LMC, SMC, M31 and M33 which are prominently visible in the GDR1 panel of Figure 2 and not in our mock catalog.

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To produce extinction estimates, we approximated each star from Galaxia by its nearest model in astrophysical space of a grid of isochrones (see Section 2.2). In addition, observational artifacts were not simulated in our catalog, which can affect the photometry and magnitude limits of stars close to bright sources in the real GDR2 catalog. In particular, we did not attempt to simulate the scanning law and varying magnitude completeness due to crowding issues.

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Finally, this model aims to reproduce the statistical properties of the Milky Way, not its actual properties at the star-by-star level. Hence, cross-matching of our catalog with any other catalog would be moot.